On the dynamics of Rossby algebraic solitary waves induced by large-scale topography

The study of atmospheric Rossby waves could provide a theoretical basis for weather forecasting systems. In this paper, the barotropic quasi-geostrophic model is used to discuss the nonlinear Rossby waves induced by large-scale topography under the β-plane approximation. Starting from the potential vorticity equation, the atmospheric area is divided into internal region and external region, and the perturbation expansions of the two equations are carried out by using the separate multi-scale perturbation method. The Benjamin–Ono equation describing the wave amplitude is obtained by matching solutions of the internal and external equations at the boundaries. The distributions of the perturbation stream function, the total stream function, and the vorticity are obtained. It is found that the algebraic solitary waves induced by large-scale topography do exist. Moreover, the amplitude of the nonlinear Rossby waves is affected along with the changes of topography.